تقرير
A note on the semistability of singular projective hypersurfaces
| العنوان: | A note on the semistability of singular projective hypersurfaces |
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| المؤلفون: | Mordant, Thomas |
| المصدر: | Math. Z. (2024), 306(4): Paper No. 67, 19 pp |
| سنة النشر: | 2023 |
| المجموعة: | Mathematics |
| مصطلحات موضوعية: | Mathematics - Algebraic Geometry, 14L24 |
| الوصف: | In this note, we give sufficient conditions for the (semi)stability of a hypersurface $H$ of $\mathbb{P}^N_k$ in terms of its degree $d$, the maximal multiplicity $\delta$ of its singularities, and the dimension $s$ of its singular locus. For instance, we show that $H$ is semistable when $d \geq \delta \min (N+1, s+3)$. The proof relies in particular on Benoist's lower bound for the dimension of the intersection of the singular locus $H_{\mathrm{sing}}$ of $H$ with some linear subspace of $\mathbb{P}^N_k$ associated to a one-parameter subgroup $\lambda$ of $\mathrm{SL}_{N+1, k}$, in terms of the numerical data in the Hilbert-Mumford criterion applied to $\lambda$ and to an equation $F_H$ of $H$. Comment: 17 pages. Various typos corrected and exposition in Subsections 5.2 and 5.3 improved. To appear in Mathematische Zeitschrift |
| نوع الوثيقة: | Working Paper |
| DOI: | 10.1007/s00209-024-03472-1 |
| URL الوصول: | http://arxiv.org/abs/2312.09774 |
| رقم الأكسشن: | edsarx.2312.09774 |
| قاعدة البيانات: | arXiv |
| DOI: | 10.1007/s00209-024-03472-1 |
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